Sieve.java Source code

Introduction

Here is the source code for Sieve.java

Source

/*
 * Copyright (c) 2000 David Flanagan.  All rights reserved.
 * This code is from the book Java Examples in a Nutshell, 2nd Edition.
 * It is provided AS-IS, WITHOUT ANY WARRANTY either expressed or implied.
 * You may study, use, and modify it for any non-commercial purpose.
 * You may distribute it non-commercially as long as you retain this notice.
 * For a commercial use license, or to purchase the book (recommended),
 * visit http://www.davidflanagan.com/javaexamples2.
 */

/**
 * This program computes prime numbers using the Sieve of Eratosthenes
 * algorithm: rule out multiples of all lower prime numbers, and anything
 * remaining is a prime. It prints out the largest prime number less than or
 * equal to the supplied command-line argument.
 */
public class Sieve {
    public static void main(String[] args) {
        // We will compute all primes less than the value specified on the
        // command line, or, if no argument, all primes less than 100.
        int max = 100; // Assign a default value
        try {
            max = Integer.parseInt(args[0]);
        } // Parse user-supplied arg
        catch (Exception e) {
        } // Silently ignore exceptions.

        // Create an array that specifies whether each number is prime or not.
        boolean[] isprime = new boolean[max + 1];

        // Assume that all numbers are primes, until proven otherwise.
        for (int i = 0; i <= max; i++)
            isprime[i] = true;

        // However, we know that 0 and 1 are not primes. Make a note of it.
        isprime[0] = isprime[1] = false;

        // To compute all primes less than max, we need to rule out
        // multiples of all integers less than the square root of max.
        int n = (int) Math.ceil(Math.sqrt(max)); // See java.lang.Math class

        // Now, for each integer i from 0 to n:
        //   If i is a prime, then none of its multiples are primes,
        //   so indicate this in the array. If i is not a prime, then
        //   its multiples have already been ruled out by one of the
        //   prime factors of i, so we can skip this case.
        for (int i = 0; i <= n; i++) {
            if (isprime[i]) // If i is a prime,
                for (int j = 2 * i; j <= max; j = j + i)
                    // loop through multiples
                    isprime[j] = false; // they are not prime.
        }

        // Now go look for the largest prime:
        int largest;
        for (largest = max; !isprime[largest]; largest--)
            ; // empty loop body

        // Output the result
        System.out.println("The largest prime less than or equal to " + max + " is " + largest);
    }
}